Math => Art

Here’s a math problem:

Given a two dimensional function (i.e. two dimensional domain, one dimensional range), how do you distribute points such that the integral of the function over the area closer to one point than any other is equivalent to the other integrals over similarly defined areas for all of the other points?

Here’s another math problem (which is slightly better known):

Given a list of cities, how should a salesman travel between all of the cities (ending up in the city he started in) so that the total trip covers the least distance?

I’m not even sure I could explain the problems to my kids, much less get them to care or understand the difficulty, or consider that there might be some sort of application.